“I can’t” is a common enough phrase. It’s supposed to indicate that something isn’t possible and usually comes with an order of “because.” It’s a phrase that has become so overused that it doesn’t have much meaning any more. When I hear it (apart from when it is used to indicate that logistics are a problem such as “I can’t at that time” or “I can’t because I’ll be doing something somewhere else” or “I’m too far away so I can’t”) I hear an echo from the Princess Bride in the background. 
“I can’t” seems to get used quite a bit to get us out of being responsible for not doing something. Instead of speaking the truth like “I don’t want to”, “That doesn’t work for me” or “I’d rather be eaten to death slowly by beetles” we use the can’t because it implies that something outside of us is the key factor and all we need to deal with is the disappointment of the other person.
“I can’t” tries to make things seem universal and permanent and monumental. I mean, that’s the theme of almost every coming of age, you can do it, inspirational, underdog does good movie, right? At some point one of the good guys says “I can’t!” and then the coach, mentor, figure of wisdom gives a speech that fires up the person or people and they find out that they can. Yay!!! “I can’t” in most cases should have “right now” connected with it or “with enough time” or “with enough resources” or “with a bit of ingenuity” or any other qualifier that actually describes the situation. I mean, I could say “I can’t goto space because I’m too old, out of shape, and not a scientist.” But Nichelle Nichols just announced that she’s going to participate in another, not the first, but ANOTHER NASA mission and she has about the same qualifications as me and almost 40 years more experience in life. So my I can’t is pretty invalid. It would be more appropriate to say that I’m not actually interested in pursuing that as there are other things I would enjoy, but I wouldn’t turn down the opportunity if it was offered. Or that I can’t right now because the opportunity isn’t in front of me right this moment, but it could be at any moment going forward.
Life is like that. There are very few absolutes. I can’t often times means I can’t the way you are asking or the way that I would like. There are usually other means to get things done, perhaps more arduous or time-consuming or needing extra resources, but they get you from here to there. So when I listen to people outlining a problem and they start shooting down solutions with “I can’t” excuses, what I hear very clearly isn’t limitation but “I don’t want to.” Which means the issue isn’t “I can’t” or even “I won’t” but that the person is invested in staying stuck in the problem. Once they can stop hugging the problem, the “I Can’t” Fallacy seems to drop away on its own and opportunities magically appear. Who knew? 🙂